Do not relinquish. It'll give you the option to move to your new plot, which will refund you 15% of the value of your old plot and transfer your house to the new one (fixtures will change size if you're moving to a bigger or small plot). All of your furniture will be put into storage, including stuff that normally can't be stored or removed once placed. You must have enough space in storage, however, which I believe is 40 outdoor and 400 indoor, no matter what plot size you're moving to.