8051 is half duplex or full duplex

No there is one SBUF write register and one SBUF read register. The two registers shares the same address.

The UART is _always_ full duplex. It is only when you connect external hardware that connects the rx and tx signals (such as in some current loops) that your software must switch between sending and receiving, to make sure that your transmissions doesn't garble any data you want to receive on the single transfer line.

No there is one SBUF write register and one SBUF read register. The two registers shares the same address.

The UART is _always_ full duplex. It is only when you connect external hardware that connects the rx and tx signals (such as in some current loops) that your software must switch between sending and receiving, to make sure that your transmissions doesn't garble any data you want to receive on the single transfer line.

"It is only when you connect external hardware..."

Without connecting external hardware, how am i going to communicate serially??

"Without connecting external hardware, how am i going to communicate serially??"

Of course, you can't!

But you entirely missed Per's point!
What he said in full was:

"It is only when you connect external hardware that connects the rx and tx signals..."

In other words, the 8051 is full duplex.
But, if you want your system to be full duplex, then you have to ensure that all parts of it can support full duplex - including your external hardware and your software.