By default Houston Centre is mission control for the ISS. Yet control
may be transferred to Moscow in case Houston centre is not available.
Houston JSC ISS MCC -- MCC-H has control for the US segment only. Roskosmos TsNIIMASH -- MCC-M has control for the Russian segment. They are interlocked.
Many ISS control systems are in the Russian segment, including attitude control and reboost (Zvezda Service Module).
Other systems (payload aboard ISS) are controlled by other control centers (ESA, JAXA, etc). There are many control centers for ISS and related elements (source: Wikipedia).
Note that ISS operations are subject to a number of ad-hoc agreements, see Wikipedia - Politics of the International Space Station. One agreement states than each module of the ISS remains under the control of the owning state.
How is control transferred? Is it merely a hand-off the way an aircraft
is transferred from one tower to another?
Aircrafts are handed off between Area Control Centers (not Towers which are used for ATC in the vicinity of the airport only), but ATC is not monitoring the aircraft functions, only the aircraft position and altitude. ATC is not responsible for flying the aircraft or performing navigation. Services provided are information, collision avoidance, and SAR. Hand over consists merely on transferring data about crossing of control points time and altitude, which is performed using computer networks.
On the other hand Mission Control Centers for the ISS monitor ISS position, systems status and alerts. In addition MCC are able to switch and command most systems aboard.
As there are systems in both ISS segments, both MCC and related control teams are already interlocked. Aboard ISS critical systems control can be transferred from one segment to the other. From Nasa:
There are data and voice links for direct communication between the control centers. Additionally, there is overlap in both control center manning and vehicle segment control.
Support groups work in each center. There is a Houston Support Group that works in MCC-M, and a Russian Support Group that works in MCC-H. These groups provide a working-level interface between the different control centers.
At all times, MCC-M and MCC-H can interface on a higher-authority level through the flight directors.
What are the mission control backup options on a
For spacecrafts other than the orbital station (ISS visiting vehicles, rockets, satellites, science probes, etc), I believe the organization remains at discretion of the operator. Operators may rely on ground segments which are more or less control rooms, transmitters and antennas, and networks on the ground. Those ground segments may serve multiple operators and spacecrafts at the same time.
A couple of ground segments:
Intelsat: Spacecraft operations are controlled through ground stations in Hagerstown, Maryland (USA), Riverside, California (USA), and Fuchsstadt, Germany. (source: Wikipedia). Services provided include backup centers (source: Intelsat).
Globalstar (aeronautical communications) use a Thales infrastructure, which includes a control center backup: "Globalstar has a 24/7 fully operational back up Ground Control Operations Center in El Dorado Hills in the event of an outage at its primary GOCC facility" (source: Globalstar).
Is there legislation making it mandatory for a satellite/launch
vehicle owner/provider to have a fully manned back-up control center?
Laws for space operations are in their infancy -- after all, space operations have been conducted for a long time by State organizations only, -- though treaties have been agreed as soon as Sputnik 1 was launched. One of them states that the launcher of a space object is liable for any damages it causes.
I don't think they are treaties or local regulations for having backup control centers.
For additional information, see: