Masters are called either 'Master(ohrly?)' or 'Guides'. Slaves are called 'Guidees', 'Slaves' or 'things/property'(this one is rude and considered to be a slur).
Slaves belong to the Crown and not to the monsters themselves. Masterless Slaves are expected to run errands in random houses and workplaces.
Each monster is allowed to be assigned as many humans as they are able to take care of. It's rare, however, for them to have more than one.
Some monsters, with a high empathy level, are able to have several Guidees. Notoriously Toriel and Papyrus.
Masters are expected to take care of their Slaves financially, providing them with food, clothes and proper sleeping conditions.
Only one Slave is allowed to sleep in the same house as their Master, others go to the main dorm with Masterless Slaves.
Masters and slaves are connected by a special type of gem named 'linkstone'. Linkstones are produced after a brief soul scan. The Master's linkstone will have the Slave's soul color and the Slave's linkstone will have the Master's magic color. Linkstones are usually wore attached to bracelets, but rings, necklaces, collars and tiaras are very common as well.
Relationships between Masters and Slaves are not forbidden by laws, but are frowned upon and considered taboo, as any teacher/student relationship would.
Physical punishment is completely forbidden, however, restrictive magic spells may be used during a life-threatening situation.
Slaves may have relationships with each other with the permission of their masters, but can't have offspring.
Misbehaving slaves have a certain amount of strikes they can get before being trapped in the Maze Tower. The amount of strikes depends on stats, soul type and NDV(Natural disposition for Violence) level. An obedient and pacific slave will have more chances to be forgiven than a bratty, difficult one.
A Master who abuses their slave(physically or mentally) will be going to trial to explain themselves. The punishments delivered onto them will vary accordingly to this scale:
Unintentional to light abuse: Will be suspended from having their slave for an amount of time, then will be put on probation to confirm if they are able to keep Mastering. If not, they will lose their slave and won't be able to register another one.
Moderate abuse or recurring abuse: Will be forbidden to have any slaves for a certain amount of time.
Heavy abuse or Moderate abuse of multiple slaves: Will be banned of having slaves indefinitely.
Heavy abuse of multiple slaves or murder of a slave: Will be locked up on the Maze Tower. The sentence will take up a month to be executed and during this time, they have the chance to appeal to the court.